It is known in the prior art to establish a safe speed profile in relation to the moving cars of a train in accordance with known track conditions, including grades, curves, stations, switches and the like. That profile and the provided track signal block circuits are determined by the track plan layout of the system, and the safe speed profile is employed to determine the command speed for each track circuit. These command speeds are based on worst case calculations of a train going through the track system with one brake failure on the train.
A brake assurance control system was added to the North-South line of Sao Paulo, Brazil, as set forth in a published article entitled "Sao Paulo Metro E-W Line Modifications" in the Conference Record of the IAS Annual Meeting of the IEEE Industry Applications Society for October 1977. An accelerometer was put on the car for operation with the brake control system in relation to the tachometer output and the change of commanded speed. The safe velocity profile determination utilized the commanded speed, the accelerometer output and information from the brake lines. A mathematical model of deceleration versus time was established, assuming various time delays in applying this deceleration, and desiring the brake rate to be minus 1.0 meter per second squared. The train deceleration rate from this model was compared with the output of a pendulum accelerometer to compute the deceleration error. The deceleration error was integrated assuming zero initial conditions, to give velocity error, and the velocity error was integrated assuming zero initial conditions to give the distance error. Each of these errors was compared with a respective reference threshold and if it got within a predetermined tolerance, the brake control applied the brakes, and the automatic train control equipment opened the speed control loop to result in the train losing system throughput performance.